We propose a stable non-parametric algorithm for the calibration of pricing models for portfolio credit derivatives: given a set of observations of market spreads for CDO tranches, we construct a risk-neutral default intensity process for the portfolio underlying the CDO which matches these observations, by looking for the risk neutral loss process ’closest’ to a prior loss process, verifying t...

In this paper, we present a multi-name incomplete information structural model which possess the contagion mechanism and its efficient Monte Carlo algorithm based on Interacting Particle System. Along with the Credit Grades, which is industrially used single-name credit model, we suppose that investors can observe firm values and defaults but are not informed of the threshold level at which a f...

In credit risk modelling, the correlation of unobservable asset returns is a crucial component for the measurement of portfolio risk. In this paper, we estimate asset correlations from monthly time series of Moody’s KMV asset values for around 2,000 European firms from 1996 to 2004. We compare correlation and value-atrisk (VaR) estimates in a one–factor or market model and a multi-factor or sec...

This paper utilizes the saddlepoint approximation as an efficient tool to estimate the portfolio credit loss distribution in the Vasicek model. Value-atrisk (VaR), the risk measure chosen in the Basel II Accord for the evaluation of capital requirement, can then be found by inverting the loss distribution. The VaR contribution (VaRC), expected shortfall (ES) and ES contribution (ESC) can all be...

We generalize the Piterbarg [1] model to include (1) bilateral default risk as in Burgard and Kjaer [2], and (2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options and barrier options taking CVA-FVA into account. We highlight the importance of this work in the context of...

We consider mathematical models for portfolio credit risk. We analyze the mathematical structure and in particular the modelling of dependence between default events in these models and propose extensions of standard industry models. We study the model risk related to the choice of model structure and input parameters. Finally we develop and test several approaches to model calibration in credi...

We provide a concise exposition of theoretical results that appear in modeling default time as a random time, we study in details the invariance martingale property and we establish a representation theorem which leads, in a complete market setting, to the hedging portfolio of a vulnerable claim. Our main result is that, to hedge a defaultable claim one has to invest the value of this contingen...

claimant and defendant’s presence has different consequences and sanctions if the legislator said that their default is not an obstacle for proceeding. current remedy is annulling the claim or default judgment. this remedy is different in the previous islamic law and our past laws and french law. the notion of presence in islamic law is personal presence and so is different from its current not...